Jet fragmentation functions are an example of an observable that cannot be calculated with four-momentum subtraction in a meaningful way, because it only works at the level of jets and not for hadron distributionsSome results were shown in [1]}, but there only the jet \(p_\perp \)  was subtracted while the hadron distribution was not and contained the full recoil contribution. The MC results therefore overshooted the data in the soft part of the fragmentation function.. It characterises the momentum distribution of charged hadrons found within \(\Delta R < R\)  of the jet axis in terms of their \(p_\perp \)  or the longitudinal momentum fraction
\( z = \frac{p_\perp ^\mathrm {(track)}}{p_\perp ^\mathrm {(jet)}} \cos \Delta R \quad \text{or} \quad \xi = \ln (1/z)\,. \) 
